The volume of a sphere is `1.76 cm^3`. The total volume of 24 such spheres with due regard to the significant places is 

Options

A. `0.42 xx 10^2 cm^3`
B. `43 cm^3`
C. `42.42 cm^3`
D. `42.2 cm^3`

Answer

To find the total volume of 24 spheres given that the volume of one sphere is \(1.76 \, \text{cm}^3\), we can follow these steps:

### Step 1: Calculate the total volume of 24 spheres
The total volume \(V\) of 24 spheres can be calculated using the formula:
\[ V = n \times V_{\text{one sphere}} \]
where \(n\) is the number of spheres and \(V_{\text{one sphere}}\) is the volume of one sphere.

Given:
- \(n = 24\)
- \(V_{\text{one sphere}} = 1.76 \, \text{cm}^3\)

Substituting the values:
\[ V = 24 \times 1.76 \, \text{cm}^3 \]

### Step 2: Perform the multiplication
Now, we perform the multiplication:
\[ V = 24 \times 1.76 = 42.24 \, \text{cm}^3 \]

### Step 3: Determine significant figures
The volume of one sphere \(1.76 \, \text{cm}^3\) has three significant figures. When performing multiplication, the result should be expressed with the same number of significant figures as the measurement with the least number of significant figures.

Since \(1.76\) has three significant figures, we need to round \(42.24\) to three significant figures.

### Step 4: Round to three significant figures
The number \(42.24\) rounded to three significant figures is:
\[ 42.2 \, \text{cm}^3 \]

Thus, the total volume of 24 spheres, expressed with the correct number of significant figures, is:
\[ \boxed{42.2 \, \text{cm}^3} \]

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